Work

Assessing the difference between integrated quantiles and integrated cumulative distribution functions

Year: 2022

Type: preprint

Abstract: This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various perspectives. The invention helps to avoid a number of technical assumptions that have been traditionally imposed when working with quantities containing quantiles. In particular it helps to completely avoid the requirement of the existence of a probability density function. The developed results explain and illustrate the invention, whose byproducts include the assessment of model uncertainty and misspecification, and the derivation of statistical inference results.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2210.16880

Authors: Wei, Yunran, Zitikis, Ricardas

Institutions: Carleton University, Western University, York University

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Mitacs, Natural Sciences and Engineering Research Council of Canada

Awards: G2614460161, Statistical Modelling of Risk Functionals, G4998900716, Automated Statistical Techniques for Systematic Anomaly Detection in High Frequency Data

OpenAlex ID: W4307929908

Cites:

Cited by: 3

Related to: 10